This paper considers the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. Set membership filter (SMF) is a popular algorithm to solve this problem. In set setting, we investigate where requires be constrained by linear or equality. We propose consensus alternating direction method of multipliers (ADMM) based SMF systems. To deal difficulty nonlinearity, in...

In this paper, we introduce the new definition of rough membership function using continues and discuss several concepts properties continuous set value functions as results on . Moreover, extend to topology spaces by substituted an equivalence class prove some theorems certain types more general fundamental generalized sets. Our result concept valued theory.

This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the cent...

Many applications of fuzzy set theory require defuzzification and ranking approaches based on alpha level sets because exact membership functions may not always be available. In this article, we have assumed that exact membership functions can be approximated using piecewise linear functions based on alpha level sets and derived two analytical formulas to meet such a requirement. The two formul...

Fuzziness plays an essential role in the real world. Fuzzy set theory has been developed very fast since it was introduced by Zadeh (1965) [1]. A fuzzy set was characterized with its membership function by Zadeh. The term fuzzy variable was fist introduced by Kaufmann (1975) [2], and then appeared in Zadeh (1978) [3] and Nahmias (1978) [4] as a fuzzy set of real numbers. In order to establish t...